Control of Conservation Laws in the Nonlocal-to-Local Limit
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908571765047296 |
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| author | Friedrich, Jan Herty, Michael Nocita, Claudia |
| author_facet | Friedrich, Jan Herty, Michael Nocita, Claudia |
| contents | We analyze a class of control problems where the initial datum acts as a control and the state is given by the entropy solution of (local) conservation laws by a nonlocal-to-local limiting strategy. In particular we characterize the limit up to subsequence of minimizers to nonlocal control problems as minimizer of the corresponding local ones. Moreover, we also prove an analogous result at a discrete level by means of a Eulerian-Lagrangian scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Control of Conservation Laws in the Nonlocal-to-Local Limit Friedrich, Jan Herty, Michael Nocita, Claudia Optimization and Control Analysis of PDEs 35L65, 49J20, 65M08 We analyze a class of control problems where the initial datum acts as a control and the state is given by the entropy solution of (local) conservation laws by a nonlocal-to-local limiting strategy. In particular we characterize the limit up to subsequence of minimizers to nonlocal control problems as minimizer of the corresponding local ones. Moreover, we also prove an analogous result at a discrete level by means of a Eulerian-Lagrangian scheme. |
| title | Control of Conservation Laws in the Nonlocal-to-Local Limit |
| topic | Optimization and Control Analysis of PDEs 35L65, 49J20, 65M08 |
| url | https://arxiv.org/abs/2510.00677 |